{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Here we check the validity of the approximation in Appendix A of docs/CNV/archived/archived-CNV-methods.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.stats import gamma\n",
    "from math import sqrt, exp, log\n",
    "from scipy.special import gammaln\n",
    "import scipy.special\n",
    "import scipy.integrate as integrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# alt minor likelihood of a alt counts and r ref counts \n",
    "# given bias ~ Gamma(alpha, beta) and minor allele fraction f\n",
    "def exact_likelihood(bias, alpha, beta, f, a, r):\n",
    "    gamma_dist = gamma(alpha, loc = 0, scale = 1/beta)\n",
    "    prefactor = gamma_dist.pdf(bias)\n",
    "    numerator = (f**a) * ((1-f)**r) * (bias**r)\n",
    "    denominator = (f + (1-f)*bias)**(a+r)\n",
    "    return prefactor * numerator / denominator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#the numerical integral over bias of the exact likelihood\n",
    "def exact_likelihood_marginal(alpha, beta, f, a, r):\n",
    "    return integrate.quad(lambda bias: exact_likelihood(bias, alpha, beta, f, a, r), 0, 10)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def approximate_likelihood(bias, alpha, beta, f, a, r):\n",
    "    n = a + r\n",
    "    w = (1-f)*(a - alpha + 1) + beta*f\n",
    "    lambda0 = (sqrt(w * w + 4 * beta * f * (1 - f) * (r + alpha - 1)) - w) / (2 * beta * (1 - f))\n",
    "    \n",
    "    y = (1 - f)/(f + (1 - f) * lambda0)\n",
    "    kappa = n * y * y - (r + alpha - 1) / (lambda0 * lambda0);\n",
    "    \n",
    "    rho = 1 - kappa * lambda0 * lambda0\n",
    "    tau = -kappa * lambda0\n",
    "    \n",
    "    logc = alpha*log(beta) - gammaln(alpha) + a * log(f) + r * log(1 - f) + (r + alpha - rho) * log(lambda0) + (tau - beta) * lambda0 - n * log(f + (1 - f) * lambda0)\n",
    "    \n",
    "    return exp(logc) * (bias ** (rho - 1)) * exp(-tau*bias)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#the analytic integral over bias of the approximate likelihood\n",
    "def approximate_likelihood_marginal(alpha, beta, f, a, r):\n",
    "    n = a + r\n",
    "    w = (1-f)*(a - alpha + 1) + beta*f\n",
    "    lambda0 = (sqrt(w * w + 4 * beta * f * (1 - f) * (r + alpha - 1)) - w) / (2 * beta * (1 - f))\n",
    "    \n",
    "    y = (1 - f)/(f + (1 - f) * lambda0);\n",
    "    kappa = n * y * y - (r + alpha - 1) / (lambda0 * lambda0)\n",
    "    \n",
    "    rho = 1 - kappa * lambda0 * lambda0\n",
    "    tau = -kappa * lambda0\n",
    "    \n",
    "    logc = alpha*log(beta) - gammaln(alpha) + a * log(f) + r * log(1 - f) + (r + alpha - rho) * log(lambda0) + (tau - beta) * lambda0 - n * log(f + (1 - f) * lambda0)\n",
    "    \n",
    "    return exp(logc + scipy.special.gammaln(rho) - rho * log(tau))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#we compare the approximate and exact distributions visually"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def compare_plot(alpha, beta, f, a, r):\n",
    "    bias = np.linspace(0, 2, 1000)\n",
    "    f_exact = lambda bias: exact_likelihood(bias, alpha, beta, f, a, r)\n",
    "    f_approx = np.vectorize(lambda bias: approximate_likelihood(bias, alpha, beta, f, a, r))\n",
    "    exact = f_exact(bias)\n",
    "    approx = f_approx(bias)\n",
    "    plot(bias, exact)\n",
    "    plot(bias, approx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def compare_marginal(alpha, beta, f, a, r):\n",
    "    exact = exact_likelihood_marginal(alpha, beta, f, a, r)\n",
    "    approx = approximate_likelihood_marginal(alpha, beta, f, a, r)\n",
    "    rel_error = (exact - approx)/exact\n",
    "    return rel_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(None, 0.0009085920076487772)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RUsDa3Sp3Eb9RuftATX0drSm1XFAwIu7bzh8corRaZ8yI+I3K3QfW7aoi+WQuAwbE4Vc6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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1054f1400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(compare_plot(40, 70, 0.3, 10, 15), compare_marginal(40, 70, 0.3, 10, 15))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(None, 0.002704597536605469)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DdiJ1PVr6XmrmtpnEfPskPXvaTqJ8RbMKzQgPepOAx9szdPgF1q2znUhdi5a+\nF9p8bDNHzv5J/hNtuOce22mUL+l3Rz9aVb+HqoO68ujjyezbZzuRSktL3wtN2TyF0keepm9vfz1h\nRrmUiDAheAIFCl+h/qCXeeghOHPGdiqVmr6R62VOXzxNtYnVSRl/gMN7SlCsmO1EyhedSzhH09lN\nqXL8JRJ+fIq1ayFQP7vHqfSNXAVcvc5OtaT2PBKsha/sKZq3KKu7rWZ7sdeRqt/w2GOQnGw7lQIt\nfa+SnJLMtC3TiF7dn759badRvq5G8Ros6biEPbW7cjQpkn799Br87kBL34usObCGwKSSFL90B02a\n2E6jFLSo0oLJIZM50jyEH/f8Rni47UQqwHYA5TyTN08m/57+9OqjVzxU7iP01lBOxZ9iXEBr5s/6\nkZIlb6J/f9upfFem9vRFJFhE9onIAREZfJ0xEx3rI0Wkfqrlc0TkpIhEOSu0+redJ3ey43gUh1Z3\nISzMdhql/mlA4wE8ensXCvZ9kJFj45gzx3Yi35Vh6YuIPzAZCAZqA91EpFaaMSFANWNMdaA3MC3V\n6g8d91U56P2f36dGzDP0CsujZ+Aqt/RWi7doXLEuFQe35/XwBD76yHYi35SZPf3GwEFjzGFjTCKw\nBGifZkw7YB6AMWYjUERESjtu/wCcc15kldaxC8f4bN8qds3twzPP2E6j1LX99Rm7N5csQ9VXOzD4\ntUssWmQ7le/JTOmXA46kun3UsSyrY1QOmbRpEnWlO63uKkalSrbTKHV9/n7+zO0wlwo3FaP664/w\nwsuXWbrUdirfkpnSz+xBVmnfOtSDs1wg9nIss7bN4vDi53n+edtplMpYgF8A8x+eT8mi+aj5Rmee\ne+EKc+faTuU7MnP0zjGgQqrbFbi6J5/emPKOZZkSnuo4rqCgIIKCgjJ7V583c9tMauZpyZXcVWjW\nzHYapTInwC+AxR0XE7oilNrhnRg6bBnnzwfy3HO2k7mviIgIIiIisv04GV6GQUQCgP1AS+A4sAno\nZozZm2pMCDDAGBMiIk2B8caYpqnWVwZWG2Nuu8bj62UYblBCYgI3T7yZEmu/5PX/1CU01HYipbLm\nSvIVnvj0CQ6fjubPCat4PLQgb76phxxnRo5dhsEYkwQMANYCe4Clxpi9ItJHRPo4xqwBDonIQWAG\n0C9VsMXAT0ANETkiInqxXyeZuW0mVfM04cofdenY0XYapbIut39uFjy8gLrlbqHAgPtYseY0zz8P\nKSm2k3l0e47XAAAL/klEQVQvveCah7qUdIlqE6tR9rtV9Hu4AT162E6k1I0zxvDq16/y6d5VFF71\nFWULlmPBAsiXz3Yy96UXXPMxs7fNpnJgfU7uaMBjj9lOo1T2iAijWo2iZ4MnOB7SjMRiOwkKguho\n28m8j5a+B7qcdJnRP47G7/s3GDQIcuWynUgp5xh01yDevf8dNtzSkhoPfknTprBrl+1U3kVL3wNN\n3TyVKnnrceC7O+jVy3YapZyra52ufNb1M74u0Iugl6fSogV8+qntVN5D5/Q9TMylGGpMqsEtG76l\nS4tbGTDAdiKlcsavZ3+l7eK23Ja/FT+Hv0f3R3Pz9tvg7287mXu40Tl9LX0P88q6V9h16DS7R81i\n/37Indt2IqVyTsylGLp/0p2TF86S65Pl5E8py6JFUKKE7WT26Ru5PuDI+SPM3DaTk0uHMWyYFr7y\nfkUCi/BZ189oV6sNv93fiOINv6NRI/jxR9vJPJfu6XuQnp/15GJ0WXZNHMHOnfpnrvItaw+uJezT\nMNoUfpH/vvESfXr7MXQoBPjop4Lo9I6X23B0Ax2XdiTfh3sZN7oQbdvaTqSU6/0e8zuPffwYkpwH\nv1XzSDxTnoULoUoV28lcT6d3vFhySjL9vuhHi6QxVKtQiAcftJ1IKTsqFalERI8IWt/Sgn33NqR6\n+xU0bgzTp+tZvJmle/oeYMqmKSyKXMG+Id/w43qhZk3biZSyb+PRjTz+yePUKnAnx+aMo6B/cWbO\nhOrVbSdzDd3T91InYk8Q/l04pbdO5okwLXyl/tKkfBO299lOldJFOd6hDhVDltL0TsOYMZCYaDud\n+9I9fTdmjKHD0g4USriNb4cOZ/duKFzYdiql3M+Goxv4z6r/UCp3FZI+m8rpQxWYOBFatrSdLOfo\nnr4XWhi1kENnf+Pn0W8wdaoWvlLX07R8U7b12ca91e9gd/P61Ht2OE/2TaBjRzh82HY696Kl76aO\nxx7nhbUv0OCPuTSsl5t27WwnUsq95fbPzRv3vsHmpzZzqeh26F+bXHVX0qChYcgQOKef1A3o9I5b\nSk5JpvWC1lT2u5vVL4azcyeUKmU7lVKe5ZvfvuG5/z5HPilKyaiRbFh2Ny+8AM8+C/nz206XfTq9\n40WGfz+cy4nJrHtjKB98oIWv1I24r8p9bO+znb5NehJV/XFqjwjhm73bqF4dJk6EixdtJ7RD9/Td\nzNeHvqb7J91puHUrlYqVYfJk24mU8nyXky4za9ssRvwwgloF7iTlu1fZ83VDnn0W+vWDokVtJ8w6\nPSPXCxw6d4i75txFaMB8Iua0YuNGCAy0nUop73Ex8SLTt0xn3IZxlA+8hYKRg9myvBVP9hIGDIBK\nlWwnzDwtfQ93LuEczeY04/7CA1j2Un9++MF3TjJRytWuJF9hya4lvPvju5Ccm3JHnmfz3M40vzMv\n/ftDq1bg5+aT31r6HuxK8hXaLGxDhdy38eVz41myBFq0sJ1KKe+XYlL48sCXTN48mc3HttDAL4wj\nn/Yh+VQN+vSBxx6D0qVtp7w2LX0PlZicSOiKUC5dgoMjV/Dyi/707m07lVK+59C5Q3yw9QM+3PEh\nFXLXIXB/D6KWdeDuxgUJC4N27SBvXtsp/0dL3wMlJifSbWU3YhMuc/S9lXTplJs33rCdSinfdjnp\nMp/u+5QFUQv44fcfqJ0rhIRNj3H46wdo3zYXHTvC/ffbf79NS9/DXEy8yKMrHyU24TJnp37KA/fl\nYfRokCz/L1RK5ZTTF0+zbPcyFkYtZO+p/VQ3DxK3tT1HI1oT3DI/HTtCcDAUKuT6bFr6HuRU/Cke\nWvwQ5fLcwq6Rs+jSKTdvvaWFr5Q7++P8H6zav4rP9n/GhiMbqep/L8l72vHbuvtpeHNlWreG1q2h\nQQPXvAmspe8hNh3bRJcVXQgq2p21Q4Yx5BXhmWdsp1JKZUXMpRjWHFjD5798zrpDX5MruRDFL7Ti\n7JZWJOxpwf13F+Oee+Duu6FOnZz5JaCl7+ZSTArjN4xn9PrRtPObzup3H2HuXGjTxnYypVR2GGOI\nOhXFukPrWHdoHT/8vp7CVKLA2WbE7LqTi/ubcXft6jS/W7jzTqhf3zkXT9TSd2NRJ6N4+ounSbiU\nQp7PF5F8pjKLFsHNN9tOppRytsTkRCJPRvLTkZ/46chPrP/9Zy4kxFP8UhOS/mjAn7vqUdrUo8kt\nVWjYwI+GDaFuXShRImvPo6XvhqLjohm9fjQLdi7krstv8+PE3gwe5MfAgb77Yc5K+aJjF46x8dhG\nIqMj2R69gy1Hd3Au4RzFrtTFRN/OuYM1yRN7CzVL3EK9qhW4tbYftWtDrVpQpsy13+/LsdIXkWBg\nPOAPzDLGvHONMROBNsBFoIcxZnsW7ut1pf/bud+YsnkKc7Z/yO2mO/tmDSGoUSlGjNC9e6XUVWcT\nzhIZHUnkyUj2nd5P1PH97D+zn9grMRRMrIacvYX4I9VJPlOJMvkqcXOxytQuV5EaVfNStSq0bZsD\npS8i/sB+oBVwDNgMdDPG7E01JgQYYIwJEZEmwARjTNPM3Ndxf68o/fOXzvP5L5+zMGohP/++mSoX\nwvht8UBaNS7P4MHQqJFrckRERBAUFOSaJ/MB+no6j76WmRN7OZZfzvzCvtP7+PXcrxz483d+Ofk7\nf1w4zOkrR8mVXJhcFytz4b1NN1T6GU0yNAYOGmMOA4jIEqA9kLq42wHzAIwxG0WkiIiUBqpk4r4e\n61LSJTYf28z6P9bz1YEINh77mVIJQcRu6EbJUyt5qGNenvwBKlZ0bS79wXIufT2dR1/LzCmYpyAN\nyzakYdmG/1qXYlKIjovm95jfafZesxt6/IxKvxxwJNXto0CTTIwpB5TNxH3dkjGGi4kXibkUw/HY\nE/xx7gSHTp1g34k/2PPnXn6L28OZpMPkj69D8uHmpPzWh3vKrqBl84IET7h6iJYec6+UcjY/8aNs\nwbKULVj2hh8jo9LP7LxLtiqu5MAHAYPB/O+/5up3yP+Wmb/j/G8s11n+v/X8e6w4Hl/+Wp5Csn88\nKQHxpPjHkRIQjyQHwuXCmAtl8LtYmtxXylBEKlA2VyjNC9WmTpnq1G8eSJ2noXJl978in1JKQcZz\n+k2BcGNMsOP2ECAl9RuyIjIdiDDGLHHc3gfcy9XpnXTv61ju+RP6SillQU7M6W8BqotIZeA40AXo\nlmbMKmAAsMTxSyLGGHNSRM5k4r43FFoppdSNSbf0jTFJIjIAWMvVwy5nG2P2ikgfx/oZxpg1IhIi\nIgeBeKBnevfNyX+MUkqp9Fk/OUsppZTruOztRxEJFpF9InJARAZfZ8xEx/pIEanvqmyeKKPXU0SC\nROS8iGx3fL1uI6cnEJE5InJSRKLSGaPbZiZk9Frqdpk1IlJBRL4Vkd0isktEnr3OuMxvn8aYHP/i\n6vTOQaAykAvYAdRKMyYEWOP4vgmwwRXZPPErk69nELDKdlZP+AKaA/WBqOus123Tea+lbpdZez1L\nA/Uc3xfg6gmv2epOV+3p/32SlzEmEfjrRK3U/nGSF1BEREq5KJ+nyczrCdk8lNZXGGN+AM6lM0S3\nzUzKxGsJul1mmjEm2hizw/F9HFdPbk17kH6Wtk9Xlf71TuDKaEz5HM7lqTLzehqgmePPvTUiUttl\n6byPbpvOo9vlDXIcCVkf2JhmVZa2T1dd6/FGT/LSd5mvLTOvyzaggjHmooi0AT4FauRsLK+m26Zz\n6HZ5A0SkALACeM6xx/+vIWluX3f7dNWe/jGgQqrbFbj62yi9MeUdy9S/Zfh6GmNijTEXHd9/CeQS\nkWKui+hVdNt0Et0us05EcgErgQXGmE+vMSRL26erSv/vk7xEJDdXT9RalWbMKiAM/j4TOMYYc9JF\n+TxNhq+niJQSuXoFIBFpzNXDc8+6PqpX0G3TSXS7zBrHazUb2GOMGX+dYVnaPl0yvWOycZKX+rfM\nvJ5AJ+BpEUni6uccdLUW2M2JyGKuXjqkhIgcAd7k6lFRum1mUUavJbpdZtVdwOPAThHZ7lj2KlAR\nbmz71JOzlFLKh+i1IZVSyodo6SullA/R0ldKKR+ipa+UUj5ES18ppXyIlr5SSvkQLX2llPIhWvpK\nKeVD/h9gbuo6KSD20AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a3e2390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(compare_plot(10, 10, 0.1, 1, 9), compare_marginal(10, 10, 0.1, 1, 9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T0brTYqwqSW7PHWAeUfY2HEv6fkVkeuIx5l4INI543AQUxWG7Mkp7bzuD9Cd1deqw/Iwo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\nXUQkhP4/WV6Mz7qWw84AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a6076a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#just comparing plots now because the quadrature runs into numerical overflow issues that are dealt with by working in \n",
    "#log space int he Java code\n",
    "compare_plot(40, 70, 0.5, 25, 17)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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23+w1tD1qDXXaIhIdsQrtesvHywSf0y6NFfC1uK+IREjX0DazMTP7vpkdNLOHzOzAFtTV\nl5U1n3wmeKc9nvNYWVOnLSLRkeq2g3Nuxcze6JzzzSwF3G1mX3POfX8L6uvJatunOBY8tCcKBVba\n6rRFJDoCTY845059q1IGSAPtoVU0gNV2jWIueGhPFjxWnTptEYmOQKFtZgkzOwgcA/7OOffD4ZbV\nn4brrdOe1OK+IhIxXadHAJxzbeAaMxsHvmxmVznnHj61/cCBA8/vWy6XKZfLIZcZTAOf8R467ZmS\nx5qp0xaR4ZudnWV2dnbgccw519sLzP4E8J1zf9r53fU6xrCM/fFuPvkL9/Fb/2p3oP3v+tl3eMN/\n+gNan/kOiVhdRyMio87McM4FWLLlTEGuHpkxs4nO4xzwS8CjvZc4fC3zmQiyQGRHMVsgka1pcV8R\niYwg0yO7gVvMLMl6yP8f59wdwy2rP62Ez6TX2801ll1fJ9LzhliYiEhIglzy9yBw3RbUMpBmq4kD\nSl468GsK6QJkalrcV0QiIzYzuX7TJ7GWJxf8m1nXV2RPVVleHl5dIiJhik1o15o1bK1AD1Pa5NN5\n2imfpaXR+CBVRKSb2IS23/Rxzd467WQiSaKd5WSlPrzCRERCFK/QbuR76rQB0q7AyYqu1RaRaIhN\naNcaPm61t04b1hf3PbGkTyJFJBpiE9oV38fW8qQC3eP5c9lEgfllddoiEg2xCe3Fmk+y3ePcCDCW\n8JjXNX8iEhGxCu2U6z208ymPBV/X/IlINMQmtCt+f6FdzJSo1BXaIhIN8Qnteo2M9R7apWyJysrS\nECoSEQlfbEJ7qe73FdoTuRLVpkJbRKIhNqG9vOKTTfYe2pP5ErU1hbaIRENsQru66pNLBl+J/ZRp\nr0S9rdAWkWiIWWj33mnvKJVYcQptEYmG2IS23/TJpfsI7fESDVNoi0g0xCq0C5neQ3vGK+EyS6ys\nDKEoEZGQxSa062v9hXYpWyKZX2JJzbaIREBsQnulVcPL9hfaidwSlcoQihIRCVlsQnu17VMa6y+0\nyarTFpFoiFVoF3v9XlbWQ7udUactItEQm9BuUGMiX+z5dcVMkVZyiUpFS46JyOiLTWg3qTKZ93p+\nXTaVxUhwcnF1CFWJiIQrPqGdqDLp9X5HJECWEscrmtQWkdHXNbTN7CIz+5aZPWxmD5nZ+7eisF60\nXZtWosZUsc/QtiInlxXaIjL6gizO1QR+zzl30Mw84Edm9g3n3KNDri2werNOoj1GsZDs6/W5RIm5\nqkJbREZf107bOXfUOXew87gKPApcOOzCelFtVLGm1/NK7Kd4qRLzNYW2iIy+nua0zWwfcC3w/WEU\n069ToV3ob3aEYqbEgq/QFpHRF3jt8s7UyJeAD3Q67ucdOHDg+cflcplyuRxSecFUG1Vo9N9pj+dK\nHKsrtEVkeGZnZ5mdnR14nEChbWZp4G+Av3TO3X729tNDeztUG1XaK/132lP5Eo+vKrRFZHjObmhv\nuummvsYJcvWIATcDjzjnPt7XuwzZ8up6aPdxQyQA08USVa1eIyIREGRO+7XAu4E3mtn9nZ/9Q66r\nJ4t+FVvzSAWe7DnTjlKJekuhLSKjr2vMOefuZsRvwpmrVkm3e78b8pSdpRKrdoRWC5L9XTUoIrIl\nRjqMg1qoVUm7/kN7MjdBprjI4mKIRYmIDEEsQnvRr5JhkNCeJOktMD8fYlEiIkMQm9AeSwwQ2mOT\nJAoLLCyEWJSIyBDEIrQrfpVccrBO22UV2iIy+mIR2ksrVQrp/kN7KjdFK6PpEREZfbEI7eVGlUJm\nsOmRZnKB+XkthCAioy0WoV1tVCll+w/tbCpLghRH52shViUiEr5YhLa/VqM4QGgD5BOTHKtoUltE\nRlssQru+VmWij6XGTldMTXFUoS0iIy4eod1eYrIwWGiPZyc5vqzQFpHRFovQXqHCtDc+0BjTuUnm\nagptERltsQjthlXYURwstHcUJ1lYUWiLyGiLfGg3W03a1mCm1OeXaXfsmphkuakLtUVktEU+tCur\nFZJr45RKNtA4F5TWb7Dx/ZAKExEZguiH9kqFRGOcYnGwcaZyk4xNLnDiRDh1iYgMQ/RDe7WCrY7j\nDXbxCDP5GdLjJxXaIjLSoh/aKxXcyuCd9o78Dsw7odAWkZEW/dBerdDyQwjtwg7aY8cV2iIy0iIf\n2gv1Cq3aeN8rsZ+ys7CTZlqdtoiMtsiH9vGlRVJr4wOv7Tidm2YlMc/xE+1wChMRGYLIh/bJ5QpZ\nBruxBiCdTDNmRZ4+oWu1RWR0RT6056oVxpgIZayp7E6emdf8iIiMruiHdq1CITV4pw3rH0YeqRwP\nZSwRkWHoGtpm9lkzO2ZmD25FQb1aqFcoZcIJ7d2lHZyoqdMWkdEVpNP+HLB/2IX0q7JSYSIXTmjv\nndpJPXGClZVQhhMRCV3X0HbO3QWM7NffLTUqTOXDCe2d+R14FxznyJFQhhMRCV3k57Sra4tMF8L5\nIHJnYSdj0wptERldqTAGOXDgwPOPy+Uy5XI5jGEDqbXn2D0+E8pYu4u7SY5/S6EtIqGbnZ1ldnZ2\n4HFCD+2t1Gq3WGGR3ROToYy3p7iHVuFZnn02lOFERJ53dkN700039TVOpKdHFlcWSbdLTE0OeDtk\nx97SXuqpw+q0RWRkBbnk71bgu8BLzOwZM3vv8MsK5qR/klRjhslwGm12ebuocYKnnl4LZ0ARkZB1\nnR5xzr1rKwrpx1x9jsTqNBPhfA5JOplmMjvD488dBfaGM6iISIgiPT1y0j+Jq82EFtoAe8f3cmju\ncHgDioiEKNKhPefP0axMs2NHeGNeMrWX1eyzLC2FN6aISFgiHdrHqidpVmaYmgpvzD3FPUz+k8Mc\nOhTemCIiYYl0aD998jh5ZkiE+G+xt7SXwu7D/PSn4Y0pIhKWSIf2MwtHGU/sDnXMi8cvJjH5M4W2\niIykSIf2keXnmM6GG9qXTl2Kn3ucJ58MdVgRkVBEOrSP+8+xqxBuaF82fRnz7gkefcyFOq6ISBgi\nHdrzzaNcWNoV6pgTYxPkMmM88ORRnHJbREZMZEN7dW2VlfYyF81Mhz725TOX0Sw9znEtYiMiIyay\noX20epSx1k727gn/X+Gy6cvYddXjPPRQ6EOLiAwksqF9eOkw6ZU97B3C3eaXTl6Kd/ETCm0RGTmR\nDe2nFp+ChUuGEtpX7riStcmHeeCB8McWERlEZEP70OIhVo4OJ7Sv230dxxL3cc894Y8tIjKIyIb2\n4ycO0Tp5Sai3sJ+yb2IfTXyenj/G/Hz444uI9Cuyof2T40+xI30JZuGPbWZct/s6Ln39fXz3u+GP\nLyLSr8iG9pOLT/DiyRcNbfyX7345k1f+iLvvHtpbiIj0LJKhvbS6RKUxxzX7Lhnae7xq76vwZ77D\nnXcO7S1ERHoWydB++PjDjDeu4PKXDK/8Gy65gUer3+Hw0bq+plVERkYkQ/uh4w+RnHspl18+vPeY\nGJvg6guu5uVvv4uvfGV47yMi0otIhvYPj9zL0k+u5aqrhvs++y/dT+7qO7jlFvQ9JCIyEiIZ2n//\n+LcpLbyBCy8c7vu846p38N3lW6murOoDSREZCZEL7aPVoxyrHeP1l79s6O912fRlvGzny3j9b9/G\nRz+qbltEtl/X0Daz/Wb2mJk9bmb/YSuK2sxtj97GjsX9vPH65Ja83/tf9X5+MPZRnnq6ye23b8lb\niohsaNPQNrMk8D+A/cCVwLvM7IqtKOx8nHN89r7Pc+Kbv8mv//rWvOdbX/JWLizupvyHf8aNN8Jj\njw33/WZnZ4f7Bi8wOp7h0vHcft067VcCTzjnnnLONYEvAv9i+GWd35cf+zLPHq/zpn2/ws6dW/Oe\nZsZn3voZvnr8z3nbh27hhhvgm98c3vvpP4pw6XiGS8dz+3UL7T3AM6f9frjz3JZyzvG3P/lbfuu2\nG6n/9af4r/9la6ZGTtk3sY87330n325/hH0f/Je860++zg37q3z+8+udd6u1peWIyAtYqsv2QB+9\n7fy9t+A6/8N1/kmP/7Sf//7zbW0cjmbuMPg7mPnBF/nCx1/HFdswQfPSnS/l4I0Hufm+m/li4SPc\n/ey9fPfJEu7+XTT8HOlElkwyQ9JSJMxIJMCMM74bxdjki1I6O9bu+QmfrNzb2f/n/y/9qd7zYz5V\n+dF2lxEbOp7bz9wml0SY2auBA865/Z3f/xBoO+f+22n76JoKEZE+OOd67sq6hXYK+DHwi8AR4AfA\nu5xzj/ZbpIiI9G/T6RHn3JqZ/S5wJ5AEblZgi4hsn007bRERGS2B74gMcpONmf15Z/s/mtm14ZUZ\nP92Op5mVzaxiZvd3fv54O+qMAjP7rJkdM7MHN9lH52ZA3Y6nzs3gzOwiM/uWmT1sZg+Z2fs32C/4\n+emc6/rD+tTIE8A+IA0cBK44a5+3AHd0Hr8K+F6QsV+IPwGPZxn46nbXGoUf4PXAtcCDG2zXuRnu\n8dS5GfxY7gKu6Tz2WP+McKDsDNppB7nJ5m3ALZ0/CL4PTJjZBQHHf6EJetOSrvcLwDl3F7CwyS46\nN3sQ4HiCzs1AnHNHnXMHO4+rwKPA2V9119P5GTS0g9xkc759hrBWeiwEOZ4OeE3nr0t3mNmVW1Zd\n/OjcDJfOzT6Y2T7W/wbz/bM29XR+dru55pSgn1ae/aevPuU8vyDH5T7gIuecb2ZvBm4HXjLcsmJN\n52Z4dG72yMw84EvABzod9zm7nPX7hudn0E77WeCi036/iPU/DTbbZ2/nOTlX1+PpnFt2zvmdx18D\n0mY2tXUlxorOzRDp3OyNmaWBvwH+0jl3vu8K7en8DBra9wKXmdk+M8sA7wC+etY+XwXe0yny1cCi\nc+5YwPFfaLoeTzO7wGz93nYzeyXrl2fOb32psaBzM0Q6N4PrHKebgUeccx/fYLeezs9A0yNug5ts\nzOx3Ots/7Zy7w8zeYmZPADXgvUH/xV5oghxP4DeAf2tma4APvHPbCh5xZnYrcD0wY2bPAB9m/aoc\nnZt96HY80bnZi9cC7wYeMLP7O8/9EXAx9Hd+6uYaEZEIidxyYyIiL2QKbRGRCFFoi4hEiEJbRCRC\nFNoiIhGi0BYRiRCFtohIhCi0RUQi5P8DTIfy1fwccz4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a623dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_plot(10, 10, 0.1, 100, 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mv6sRCU7hLn3S0tbCpv2bqF0zl9mz/a4mci7KuYhXtr/CZZ9zPK8bWksMULhL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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a74c400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_plot(10, 10, 0.3, 100, 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tH0WRX9rR9zGVhISWl//9MkUvOs5Fd71AmzYQH5/1j6k1CslxDp06RKXhVSk8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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a6284e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_plot(10, 10, 0.5, 0, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pSPuN++jYtjQvvmg7kVLuISIYYwo0jqtnIHvIzpM7Cc+sQpcoLQS+qmFEQ7rX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\nKbQYKKWUAv4PczgfHXiQwmIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a6bbf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_plot(10, 10, 0.5, 10, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Kvvj6C8pi9zF2rJ25GNNcWHJpADmFObQ43K9Zj7dUatuiLRNSJ/DO5neYOhVe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\neapfmxsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a609358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_plot(10, 10, 0.2, 10, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SDhoMf5WEBNtplLto6Xu58cvmUtHZnpw5bSdRgcYR5CB6wMccKfke3SNX2I6j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\nREtfKaUCiJa+UkoFEC19pZQKIP8H7LyPDCkkud0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a6a7a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_plot(10, 10, 0.2, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3.0
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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